Although it has little relation to antioxidant activity, it's hard to beat their omega 3 essential fatty acid content. Do flaxseeds contain more omega 3 than salmon? Yes, that is not a rumor. For example, both fresh water and marine sockeye salmon have 1.3 grams of omega 3 per 100 gram serving (about a 3.5 ounce portion). Compare that to ground flaxseeds, as just two tablespoons provides 1.6 grams. That's more omega 3's even though your serving weighs 85% less. Chia seeds contain more than salmon, too.
Now it is true that the forms found in fish, EPA and DHA, are preferred over ALA, the form found in plants. However when you compare the pros and cons of vegan omega 3 sources versus fish, many conclude that plant-based sources remain the better choice, especially when consuming larger quantities because of heavy metals and other pollutants found in seafood. Organic flax oil will be your most concentrated source of omega 3 for this plant.
The amount of how much antioxidants there are in flax seeds and oil is relatively low, especially considering that the average portion consumed at a given time will not be 100 grams (which is what the ORAC scale uses). That is not necessarily a bad thing or even unusual for a seed. The primary health benefit you are getting is the high omega 3 content and relatively rich amounts of protein. The ORAC value of flaxseed should not be the reason for eating them.
Men should keep in mind that flax is the number one highest phytoestrogen food and therefore, consumption should probably be limited. On the other hand for women, especially post menopausal women, this is a top superfood.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010